8th Grade Translations, Reflections and Rotations Test Solutions and Scoring (PDF)

8th Grade math test solutions: Translations, Reflections and Rotations – Maths PDF

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This rigid transformations test answers for 8th Grade covers translations, reflections and rotations (Common Core 8.G.A.1, 8.G.A.2, 8.G.A.3), with a free PDF to print.

Use this answer key to score the translations, reflections and rotations test out of 20 points. Each solution shows the full work and a scoring guide, so partial credit can be given fairly when a student shows correct steps but makes an arithmetic slip.

Grade 8 · Common Core State Standards: 8.G.A.1, 8.G.A.2, 8.G.A.3

Rigid transformations test answers: worked solutions

Question 1 – Points [3 pts]

\((-2, 2)\)
\((-3, -6)\)
\((-1, 4)\)

Scoring: 1 point each.

Question 2 – Translate a figure [3 pts]

The image is below and to the right.

\((x, y) \to (x + 3, y – 4)\).

\(K^{\prime}(4, -3),\ L^{\prime}(8, -3),\ M^{\prime}(8, -1)\)

Scoring: 1 point for the rule, 2 points for three correct vertices (1 point if one is wrong).

Question 3 – Reflect a figure [3 pts]

Mirror image across the x-axis.

\((x, y) \to (x, -y)\).

\(W^{\prime}(-2, -1),\ X^{\prime}(-5, -1),\ Y^{\prime}(-2, -4)\)

Scoring: 1 point for the rule, 2 points for the vertices.

Question 4 – Sequence [3 pts]

Reflect: \((-2, 5)\). Translate: \((-2, 2)\).

Rotate \(180^{\circ}\): \((-2, -5)\).

Scoring: 1 point for the reflection, 1 point for the translation, 1 point for the rotation.

Question 5 – Properties [2 pts]

The image is still 6 cm by 4 cm. Side lengths and angle measures (also parallelism) stay the same.

Scoring: 1 point for the dimensions. 1 point for two properties.

Question 6 – Congruent figures [3 pts]

Yes. A translation 4 right and 2 up maps \(A\) to \(D\), \(B\) to \(E\) and \(C\) to \(F\).

Scoring: 1 point for yes, 2 points for the transformation.

Question 7 – Mirror [2 pts]

The y-coordinate is unchanged and the x-coordinate changes sign.

The y-axis

Scoring: 1 point for the observation. 1 point for the y-axis.

Question 8 – Explain [1 pt]

A reflection preserves all side lengths and angle measures, so the image has exactly the same size and shape; flipping changes only the orientation.

Scoring: Award full credit for stating that lengths and angles are preserved.

Total score

Total

20 points

Key facts behind this rigid transformations test answers

Key facts

Translation by \((a, b)\): \((x, y) \to (x + a, y + b)\).
Reflection across the x-axis: \((x, -y)\); across the y-axis: \((-x, y)\).
Rotation about the origin: \(90^{\circ}\) counterclockwise \((-y, x)\); \(180^{\circ}\) \((-x, -y)\); \(90^{\circ}\) clockwise \((y, -x)\).
Rigid motions preserve lengths, angles and parallel lines.
Two figures are congruent if a sequence of rigid motions maps one to the other.

How to use this rigid transformations test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All Grade 8 chapters: Grade 8 math.

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